Optical locker

ABSTRACT

There is described an interferometer for use in an optical locker. The interferometer comprises at least two transparent materials having different thermal path length sensitivities. The interferometer is configured such that an input beam is split by the interferometer into first and second intermediate beams, which recombine to form an output beam, the first and second intermediate beams travelling along respective first and second intermediate beam paths which do not overlap. At least one of the intermediate beam paths passes through at least two of the transparent materials. A length of each intermediate beam path which passes through each transparent material is selected such that an optical path difference between the first and second intermediate beam path is substantially independent of temperature.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/839,488, filed on Apr. 3, 2020 (now U.S. Pat. No. 11,215,440), whichis a divisional of U.S. patent application Ser. No. 16/308,545, filed onDec. 10, 2018 (now U.S. Pat. No. 10,612,906), which is a 35 U.S.C. 371national stage filing of International Application No.PCT/GB2017/051856, filed on Jun. 26, 2017, which claims priority fromUnited Kingdom Application No. GB1611194.0 filed on Jun. 28, 2016. Thecontents of the aforementioned applications are hereby incorporated byreference in their entireties.

FIELD OF THE INVENTION

The present invention relates to an optical locker. In particular, theinvention relates to improvements to an interferometer for measuringwavelength in an optical locker.

BACKGROUND

In fibre-optic communications channels, Dense Wavelength DivisionMultiplexing (DWDM) is used to transmit multiple optical signals via asingle fibre. For such applications, each of the channels has a distinctfrequency, defined by a frequency grid (e.g. ITU-T G.694.1).

The frequencies of optical signals produced by laser sources are“locked” to the frequencies of the grid by a wavelength lockingmechanism. The wavelength locking mechanism comprises a means formeasuring the wavelength of each optical signal, and a feedback loopwhich adjusts the output of the corresponding laser source in dependenceupon the measurement.

Typically, the means for measuring the wavelength comprises aFabry-Perot (FP) etalon (or interferometer). An FP etalon is illustratedin FIG. 1A, and comprises a transparent plate with two reflectingsurfaces. As the light bounces between the surfaces, the transmittedrays interfere with each other, producing a characteristic interferencepattern, which is dependent upon the frequency and the optical distancebetween the plates.

The frequency response of a FP etalon has the characteristic curve shownin FIG. 1B. To provide the greatest resolution for the optical locker,it is calibrated such that the desired frequency is in a region of thefrequency response graph with a high gradient. This means that smallchanges in the frequency will produce large changes in the output.

Since the behaviour of an etalon is dependent on the optical path lengththrough the plate, the behaviour is strongly temperature dependent. Theoptical path will tend to increase with temperature, both due to theexpansion of the material with temperature, and the change in refractiveindex of the material with temperature.

P(T) = n(T)L(T) $\alpha = {\frac{1}{L}\frac{d\; L}{T}}$$\psi = \frac{dN}{dT}$

Where P is the optical path length, n(T) is the refractive index as afunction of temperature, L(T) is the physical length as a function oftemperature, α is the coefficient of thermal expansion, and ψ is thethermo-optic coefficient. α is positive for most materials, and y may bepositive or negative.

Therefore, to ensure proper calibration, the temperature of an etalonmust be strictly controlled. This can either be done by keeping theetalon at a constant temperature. In more sophisticated etalons such asthat disclosed in WO 2015/030896, the temperature of the etalon can bevaried in a controlled manner in order to allow the etalon to beautomatically recalibrated to different frequencies.

The temperature control adds additional complexity and cost to themanufacture of the etalon, and so there is a need for an optical lockerwhich can be made temperature independent.

In order to create a temperature independent etalon (to form the basisof a temperature independent optical locker), the phase differencebetween interfering beams must be independent of temperature. In orderto achieve this, the optical path difference between the beams must beindependent of temperature.

Consider a simplified FP etalon, where there are only two transmittedbeams—a beam which passes straight through the transparent plate, and abeam which is reflected once off each interfering surface. P₁ is theoptical path length of the first beam, P₂ is the optical path length ofthe second beam, and ΔP is the optical path difference.

${\Delta\; P} = {{{P\; 2} - {P\; 1}} = {\left( \frac{2\;\pi}{\lambda} \right)\mspace{11mu} 2{nl}\;\cos\;\varphi}}$

as can be found in any textbook discussion of the FP etalon, e.g.wikipedia.org/wiki/Fabry-Perot_interferometer.

ΔP contains a contribution from the difference in path length within thetransparent plate, and a contribution from the difference of path lengthin air. The difference of path length in air is essentially constantover reasonable temperatures, so the temperature dependence comes fromthe difference in path length through the transparent material. p₁ isthe optical path length of the first beam through the transparentmaterial, and p₂ is the optical path length of the second beam throughthe transparent material. Since the first and second path pass throughthe same material, p₂=3p₁, so ΔP=ΔP_(air)+2p₁. Therefore the temperaturedependence of the path difference, dΔP/dT=2dp₁/dT, the temperaturedependence of the path through the transparent material.

dp₁/dT cannot be zero for any known material. For known materials, thechange in path length with temperature, dP/dT, is generally positive, aseven in those materials with a negative thermo-optic coefficient, theexpansion of the material itself (i.e. increase in L) counteracts thereduction in refractive index. FIG. 2 shows this—FIG. 2A shows a vs yfor a range of glasses, and FIG. 2B shows the overall thermal pathdependence for a range of glasses. Since dP/dT is positive, nocombination of materials in the transparent plate can result in dp₁/dTbeing zero.

Therefore, a temperature independent etalon is not possible.

SUMMARY

According to one aspect of the present invention there is provided aninterferometer for use in an optical locker. The interferometercomprises at least two transparent materials having different thermalpath length sensitivities. The interferometer is configured such that aninput beam is split by the interferometer into first and secondintermediate beams, which recombine to form an output beam, the firstand second intermediate beams travelling along respective first andsecond intermediate beam paths which do not overlap. At least one of theintermediate beam paths passes through at least two of the transparentmaterials. A length of each intermediate beam path which passes througheach transparent material is selected such that an optical pathdifference between the first and second intermediate beam path issubstantially independent of temperature.

According to a further aspect, there is provided a Michelsoninterferometer for use in an optical locker. The interferometercomprises a beam splitter, first and second mirrors, and at least twotransparent materials. The beam splitter is configured to split an inputbeam into first and second intermediate beams, and to recombine saidintermediate beams to form an output beam, the first and secondintermediate beams travelling along respective first and secondintermediate beam paths. The first and second mirrors are respectivelypositioned intersecting said first and second intermediate beam pathssuch that the first and second beam paths are reflected back to the beamsplitter by the first and second mirrors, and wherein the first andsecond mirrors are positioned so as to create an optical path differencebetween the first and second beam paths. The at least two transparentmaterials have different thermal path length sensitivities. A length ofeach intermediate beam path which passes through each transparentmaterial is selected such that the optical path difference between thefirst and second intermediate beam path is substantially independent oftemperature.

According to a further aspect, there is provided a Mach-Zehnderinterferometer for use in an optical locker. The interferometercomprises first and second beam splitters, at least one mirror, and atleast two transparent materials. The first beam splitter is configuredto split an input beam into first and second intermediate beams, thefirst and second intermediate beams travelling along respective firstand second intermediate beam paths. The second beam splitter isconfigured to recombine said intermediate beams to form an output beam.The at least one mirror is positioned intersecting said first and/orsecond intermediate beam paths such that the first and second beam pathstravel from the first beam splitter to the second beam splitter, andwherein the at least one mirror is positioned so as to create an opticalpath difference between the first and second beam paths. The at leasttwo transparent materials have different thermal path lengthsensitivities. A length of each intermediate beam path which passesthrough each transparent material is selected such that the optical pathdifference between the first and second intermediate beam path issubstantially independent of temperature.

According to a further aspect, there is provided an interferometryassembly for use in an optical locker. The assembly comprises an inputassembly, an interferometer, and a detector assembly. The input assemblyis configured to receive a test beam, to split the test beam into aplurality of physically non-coincident input beams, and to direct theinput beams to the interferometer. The interferometer is configured toreceive each input beam and to produce, for each input beam, an outputbeam with an intensity that depends on the wavelength of the input beam.The detector assembly is configured to produce a plurality of outputsignals, each output signal being dependent on the intensity of arespective output beam. The input assembly is configured to direct theinput beams such that each input beam travels through the interferometerwith a differing path difference, and such that the output beams arriveat the detector assembly physically separated.

According to a further aspect, there is provided an interferometryassembly for use in an optical locker. The assembly comprises aninterferometer, and a detector assembly. The interferometer isconfigured such that an image of the input viewed from the output alonga first path is displaced from an image of the input viewed from theoutput along a second path at least in a direction perpendicular to theinput beam. The detector assembly is configured to detect theintensities of different regions of an interference pattern produced bythe interferometer, and to determine a plurality of output signals onthe basis of the intensities of the regions; wherein each of the outputsignals has a different phase for the relationship between intensity andwavelength.

According to a further aspect, there is provided a method of measuringthe wavelength of a test beam. The method comprises providing the testbeam into an interferometry assembly according to either of the previoustwo aspects, and determining the wavelength of the test beam on thebasis of the output signal with the greatest rate of change withwavelength at the measured intensity.

BRIEF DESCRIPTION OF THE DRAWINGS

In the figures, where optical components are illustrated:

Double lines indicate mirrors (e.g. 303 in FIG. 3);

Thin dotted lines indicate beam splitters (e.g. 302 in FIG. 3);

Thick dotted or dashed lines indicate beam paths (e.g. 30 in FIG. 3);

Beam paths which do not contribute to the final output are not shown.

FIG. 1A shows a Fabry-Perot etalon;

FIG. 1B is a graph illustrating the frequency response of a Fabry-Perotetalon;

FIG. 2 shows thermal properties of a range of glasses;

FIG. 3 shows a Mach-Zehnder interferometer according to the prior art;

FIG. 4 shows a Mach-Zehnder interferometer according to an embodiment;

FIG. 5 shows graphs of intensity v wavelength for a selection ofinterferometers;

FIG. 6 shows example geometries of interferometers;

FIG. 7 shows graphs comparing an interferometer at exact thermalindependence with an interferometer where L₂ is 111 microns too long;

FIG. 8 shows an exemplary output from an interferometer with multipleoutput signals;

FIG. 9A and FIG. 9B show arrangements for focusing beams onto adetector;

FIG. 10 shows interference patterns for a range of interferometers;

FIG. 11A and FIG. 11B show intensity along a slice of a detector vsphase angle for an exemplary interferometer;

FIG. 12A and FIG. 12B show intensity along a slice of a detector vsphase angle for a further exemplary interferometer;

FIG. 13 shows an exemplary detector; and

FIG. 14 shows an exemplary interferometer.

INDEX OF TERMS IN EQUATIONS

Unless Otherwise Specified in the Description of the Equation

T—Temperature

P—Optical path length

L—Physical path length

α—Linear coefficient of thermal expansion

n—Refractive index

ψ—Thermo-optic coefficient

q—Thermal path length sensitivity, q=1/L dP/dT=nα+ψ

v—Frequency

λ—Wavelength

c—Speed of light in vacuum

S—output power

E—electric field strength

w—Gaussian half-width of a distribution

φ—angle (as indicated in description)

θ—phase difference

Subscripts indicate that the quantity is for a particular component oralong a particular path, unless otherwise defined. Subscripts n or xindicate a choice of component or path (e.g. n_(x) would be therefractive index of any of the materials being discussed). Δ is used toindicate a difference, e.g. ΔP is the optical path difference.

DETAILED DESCRIPTION

Temperature Independent Interferometer

In order to create a temperature independent optical locker, atemperature independent interferometer is required. As has been shownabove, this is not possible for an etalon. However, this can be achievedfor other types of interferometers.

Consider, for example, a Mach-Zehnder (M-Z) interferometer as shown inFIG. 3. An input beam 30 is split by a beam splitter 301 intointermediate beams 31 and 32. Intermediate beam 31 travels to beamsplitter 302 via mirror 303, while intermediate beam 32 is diverted bybeam splitter 301 and directed to beam splitter 302 using mirror 304. Atbeam splitter 302, the beams 31 and 32 recombine into output beam 33,and the intensity of the output is dependent upon the phase differenceof intermediate beams 31 and 32 at beam splitter 302, and therefore onthe optical path difference between the paths taken by intermediatebeams 31 and 32.

Let the path taken by beam 31 have path length P₃₁, and let the pathtaken by beam 32 have path length P₃₂.

Δ P = P₃₂ − P₃₁$\frac{d\;\Delta\; P}{T} = {\frac{{dP}_{32}}{dT} - \frac{{dP}_{31}}{dT}}$therefore $\frac{d\;\Delta\; P}{T} = 0$ if${\frac{{dP}_{32}}{dT} - \frac{{dP}_{31}}{dT}} = 0$

Since P₃₂ and P₃₁ are independent (unlike in the FP etalon, where p₂ isa multiple of p₁), this condition is possible to achieve in practice.

For example, consider the M-Z interferometer shown in FIG. 4. An inputbeam 40 is split by a beam splitter 401 into intermediate beams 41 and42. Intermediate beam 41 travels directly to beam splitter 402, whileintermediate beam 42 is diverted by beam splitter 301 and directed tobeam splitter 402 using mirrors 403. At beam splitter 402, the beams 41and 42 recombine into output beam 43, and the intensity of the output isdependent upon the phase difference of intermediate beams 41 and 42 atbeam splitter 402, and therefore on the optical path difference betweenthe paths taken by intermediate beams 41 and 42. The interferometer ofFIG. 4 has a part 421 made of a first material, and a part 422 made of asecond material. The path taken by beam 41 passes only though the firstmaterial; and the path taken by beam 42 passes through both the firstand second material.

If the first and second materials are properly selected, then adjustingthe length of the path taken by beam 42 through each of the first andsecond material relative to the length of the path taken by beam 41through the first material can give a geometry where the path differenceis thermally independent. For example, where block 421 is made from LAF9(a commercially available glass) and block 422 is made from quartz, FIG.5 shows graphs of the intensity of the output vs wavelength fordiffering ratios of physical path length. The physical path length inFIG. 5 is measured from beam splitter 401 to beam splitter 402,subtracting the distance travelled by beam 32 through block 421 todiscount equivalent parts of the paths.

In FIG. 5A, the ratio is 2.826, and the output intensity vs wavelengthgraph moves to the left with increasing temperature (i.e. the graph istranslated in the direction of lower wavelength). In FIG. 5B, the ratiois 4.355, and the graph moves to the right with increasing temperature.FIG. 5C shows the case where the ratio is 3.537—and there is no changeto the graph over a temperature difference of 50K—i.e. theinterferometer is temperature independent.

It will be appreciated that various geometries are possible which resultin temperature independence, provided that the first and second path areindependent—i.e. there is at least a part of the first path which doesnot overlap the second path, and vice versa. Some example geometriesbased on the M-Z or Michelson interferometer are shown in FIG. 6. Doublelines represent reflective surfaces, dotted lines represent beamsplitters, and thick dashed lines represent the path taken by the light(neglecting any beams which do not contribute to the interferencepattern). Each enclosed region is made from a different material. Thenon-overlapping parts of the path can be tuned to give the desiredtemperature independence, which will require that the non-overlappingparts of at least one of the paths pass through two different materials.As shown in FIG. 6D, the beam splitter can be produced by providing anair gap between the two glasses, with either a wedge or cylindricalsurface on the side of the air gap opposite the input. The partialinternal reflection on the input side of the air gap provides therequired beam splitting. The wedge or cylindrical surface ensures thatthe angle of the beam on the far side of the air gap is different to theangle of the beam on the near side of the air gap, creating the requiredpath difference.

In order to achieve a required free spectral range, as well as thermalindependence, the physical path lengths must satisfy:

${L_{1} - L_{2}} = \frac{c}{\Delta\; v}$${\sum\limits_{x}{L_{1x}q_{x}}} = {\sum\limits_{x}{L_{2x}q_{x}}}$

Where L₁ is the physical length of non-overlapping portion of the firstoptical path (i.e. the path between beam splitters); L₂ is the physicallength of non-overlapping portion of the second optical path; q_(x) isthe thermal path length sensitivity for material x, q=nα+ψ; Δv is thefree spectral range; c is the speed of light in vacuum; and L_(nx) isthe physical length of path n passing through material x.

For the interferometer shown in FIG. 4, or for other interferometerswhere the path L₁ passes through only the first material, and path L₂passes a distance L₀ through the first material, and a distance L₂−L₀through the second material, the equations reduce to those below.

${L_{1} - L_{0}} = {\frac{c}{\Delta\; v}\frac{1}{{q_{1}/q_{2}} - 1}}$${L_{2} - L_{0}} = {\left( {L_{1} - L_{0}} \right)\frac{q_{1}}{q_{2}}}$

Where q₁ is the thermal path length sensitivity of the first material,and q₂ is the thermal path length sensitivity of the second material andq=nα+ψ. Where both L₁ and L₂ pass a distance L₀ through the firstmaterial, and each then passes through respective other materials (e.g.FIG. 6X), these equations can be used with q_(n) being the thermal pathlength sensitivity for the other material passed through by path L_(n).Of course, where there is some freedom in the free spectral range, thedistance L₁ can be chosen, and the free spectral range calculated fromthat.

While the refractive index, n, is temperature dependent, q can beassumed constant since the variation in n is small (ψ is typically onthe order of 10⁻⁶ to 10⁻⁷, n is typically between 1 and 2, so fortemperature differences of around 100K, the variation is up to about0.1%). The errors introduced by this approximation are likely to benegligible—typical values for L1 and L2 are on the order of 1000microns, so the error due to any variation in q is likely to be similarto manufacturing tolerances. FIG. 7 shows graphs comparing aninterferometer at exact thermal independence with an interferometerwhere L₂ is 111 microns too long—the temperature dependence is 0.5 MHzper K per micron of error. Given that the optical locker will typicallybe operating at frequencies in the tens of GHz, this is an acceptablevariation.

Multiple Output Signals

For the optical locker to function effectively, the wavelengthmeasurement should be made at a region of high gradient of thewavelength/intensity graph. Examples are presented below of ways toachieve such sensitivity over the whole wavelength range with a singleinterferometer, even where the interferometer is temperatureindependent. It will be appreciated by the skilled person that the belowexamples do not require the interferometer to be temperatureindependent, and will work with temperature dependent interferometersprovided that the temperature is adequately controlled.

The principle of the below examples is to provide an interferometer withtwo or more output signals, where at least one of the output signals hasa high gradient at any wavelength. An example of this is shown in FIG. 8in which lines 1, 2 show first and second output signals, respectively.As shown below the graph, by varying which signal is measured dependingon the wavelength, a high degree of sensitivity can be maintained overthe whole range.

A first option to generate multiple output signals is to use multipleinput beams—the input beams are separated either vertically orhorizontally, to cause corresponding separation in output beams andallow the signal from each output beam to be resolved separately. Inorder to cause the difference in output beams, each of the input beamsmay have different angles of entry into the interferometer, therebycausing a different optical path difference for each beam. To generatethe input beams to the interferometer, the beam to be tested may besplit by one or more beam splitters prior to entering theinterferometer.

For interferometers with a sinusoidal response, such as a Michelson orMach-Zehnder interferometer, an output of two beams, with a π/2 phasedifference between the wavelength/intensity graphs of each beam givessufficient sensitivity. For other interferometers, more than two outputbeams (and hence more than two input beams) may be necessary to coverall wavelengths with sufficient sensitivity. This technique can work forany interferometer where the output signals arrive at the detectorassembly physically separated.

The physical separation can be increased by separating the input beamshorizontally and/or vertically. FIG. 9A shows an exemplaryinterferometer with vertically stacked beams in side view 901 and planview 902, and FIG. 9B shows an exemplary interferometer withhorizontally stacked beams is side view 911 and plan view 912. Eachexemplary interferometer has a pair of input beams 903 & 904, 913 & 914,which are directed into an interferometer 905, 915 (shown as a Michelsoninterferometer, though other types may be used). Each of the beams isdirected into the interferometer such that the path difference of eachbeam is different, e.g. by introducing a small angular error to eachbeam. The input beams 903 & 904, 913 & 914 produce respective outputbeams, which are focused by parabolic mirror assembly 906, 916 ontodetector assembly 907, 917. Detector assembly 907, 917 is not shown inthe plan view, as it is underneath parabolic mirror assembly 906, 916.Parabolic mirror assembly 906, 916 comprises two parabolic mirrors, onefor each beam, and detector assembly 907, 917 comprises a detector ordetector region for each beam, and produces a separate output signal foreach beam.

Alternatively, a single input beam may be used to obtain two outputsignals. This can be done by introducing a small angular error into themirrors of a Michelson or Mach-Zehnder interferometer. As can be seen inFIG. 10, instead of forming concentric circles, the interference patterntends towards a series of parallel fringes as the angular errorincreases. The change in intensity of the pattern with wavelength isless pronounced, but the pattern instead translates to either side withchanges in wavelength. The condition for the pattern to behave in thisway is that, when viewed from the output of the interferometer, theimage of the input along one beam path is displaced in a directionperpendicular to the beam path from an image of the input along theother beam path. Where the images of the input are displaced entirelyparallel to the beam path, the “classic” concentric circle fringepattern appears, and its intensity depends on the wavelength. Where theimages of the input are displaced entirely perpendicular to the beampath, the interference pattern is a series of fringes and the intensityis independent of the wavelength. Other displacements will form theintermediate patterns shown in FIG. 10, depending on the angle betweenthe beam path and a line connecting the images of the input.

FIG. 11A shows the horizontal (x) distribution of intensity across thecentre of the detector as the phase difference (θ) between the two armsis varied. The spot can be seen to displace along the x-axis and bereplaced by another spot as the phase difference changes. This happensperiodically with a period equal to the FSR. FIG. 11B shows theintegrated intensity detected by each half of the detector (i.e. x>0,x<0)—this generates two signals 1101, 1102 with a π/2 phase differenceas desired (and as discussed in connection with FIG. 8).

If the angle between the beams is increased, then fringe spacingdecreases (as described above with reference to FIG. 10), and severalintensity peaks move across the image. This is shown in FIG. 12A, whichshows the horizontal (x) distribution of intensity across the centre ofthe detector as the phase difference (θ) between the two arms is variedfor an interferometer with a greater angle between the beams than inFIG. 11A. FIG. 12B shows the integrated intensity gathered for each halfof the detector—it can be seen that this example would not be suitablefor a multiple output system, as the two signals 1201, 1202 are inantiphase, so the largest gradient of each signal occurs together. Itwill be appreciated by the skilled person that the angle between thebeams and the configuration of the regions of the detector can be variedto produce any number of signals with a desired phase difference.

Therefore, the intensity in different regions of the pattern will stillvary with wavelength. Measuring separate regions of the pattern cantherefore give signals which vary with wavelength at a constant phasedifference from each other. For example, dividing the detector intothree sections as shown in FIG. 13, and taking the two signals assig1/sig2 and sig3/sig2 will give plots with a phase displacementdependent on the width of detector 2.

Alternatively, the detector may be divided into two sections, and theoutput signals obtained from each section.

In general, to retrieve a number of output signals, the detector may bedivided into that number of segments, with one signal retrieved fromeach segment, or into a greater number of segments, with signalsobtained by combinations of segments.

The phase difference between signals can be calculated from the powerreceived at each detector.

$\mspace{79mu}{E_{tot} = {\left( {{e^{{- \frac{x}{w_{- x^{2}}}} - \frac{y}{w_{y}^{2}}}e^{{- {ix}}\;\varphi_{0}}} + {e^{{- \frac{x}{w_{\,_{- x^{2}}}}} - \frac{y}{w_{y}^{2}}}e^{i{({{x\;\varphi_{0}} + \theta})}}}} \right)E_{0}}}$$S_{tot} = {{E_{tot}\overset{\_}{E_{tot}}} = {\left( {\left( {{\cos\left( {{x\;\varphi_{0}} + \theta} \right)} + {\cos\left( {x\;\varphi_{0}} \right)}} \right)^{2} + \left( {{\sin\left( {{x\;\varphi_{0}} + \theta} \right)} - {\sin\left( {x\;\varphi_{0}} \right)}} \right)^{2}} \right)\left( e^{{- \frac{x}{w_{- x^{2}}}} - \frac{y}{w_{y}^{2}}} \right)^{2}E_{0}^{2}}}$     sigN = ∫_(−∞)^(∞)∫_(n⁻w_(x))^(n₊w_(x))S_(tot)dxdy

where w_(x) and w_(y) are the Gaussian half widths of the beam in x andy respectively, φ₀ is the directional angular separation between the twobeams, θ is the phase difference between the two beams and depends onthe frequency, E_(tot) is the total electrical field from the output,S_(tot) is the total output power, E₀ is a constant, sigN is the signalreceived from region N, and n₊ and n⁻ are the extent of the region N inthe x direction, measured in units of w_(x). The above equation gives anidealised case where the extent of the detectors in the y direction isinfinite. In a practical application where the detector extends to±Yw_(y), the final integral is:

sigN=∫− _(Yw) _(y) ^(Yw) ^(y) ∫_(n) ⁻ _(w) _(x) ^(n) ⁺ ^(w) ^(x) S_(tot) dxdy

In order to produce an output which can be used in an optical locker,the output signal must be normalised, so that the signal is dependentonly on the wavelength and not on the power of the input beam. In aconventional optical locker, this is performed by splitting the beamprior to the etalon, sending a first beam to the interferometer, and asecond beam to a detector. The output signal from the etalon is dividedby the signal from the detector to form a normalised output signal.However, this requires that a portion of the power is “siphoned off” tothe detector, and so reduces the efficiency of the optical locker.

When using a Michelson interferometer, a more efficient normalisationcan be obtained, whist also preventing the return of light to the laser.An exemplary system is shown in FIG. 14. The Michelson interferometer1401 may be temperature independent (as shown in the Figure, anddescribed above) or it may be a conventional Michelson interferometer.In addition, this may be used with the angular error in the mirrorsdescribed above. The input beam is provided polarised with an inputpolarisation, which is a linear polarisation. The beam splitter 1402 isa 100% polarising splitter configured to allow the input polarisation topass through. The reflected component of the input beam (not shown) isabsorbed by an absorbing surface, and the transmitted component passesto the interferometer 1401 via a quarter wave plate 1403, meaning thatthe light within the interferometer is circularly polarised. Theinterferometer creates two output beams—one passing to the detector1404, and another passing back along the path of the input beam. As thesecond output beam passes the quarter wave plate, it is linearlypolarised such that when it meets the 100% polarising splitter, the beamis totally reflected to the detector 1405.

The input power to the interferometer is the sum of the power at thedetectors 1404 and 1405, so the normalisation can be calculated asS₁₂₀₄/(S₁₂₀₄+S₁₂₀₅), where S is the power measured at each detector. Ifthe detectors 1404 and 1405 do not have the same sensitivity, then thenormalised signals will have a slightly non-sinusoidal relationshipbetween intensity and wavelength. This is not significant for ˜10%differences in sensitivity between the detectors, and can be correctedfor at greater differences. Similarly, the signal profile will bealtered due to any dead space between segments of a multi-part detector,but these errors can be compensated for as the effect is identical overthe band.

1-11. (canceled)
 12. An interferometry assembly, the interferometryassembly comprising: an interferometer configured to receive an inputbeam, the interferometer including a first part made of a first solidmaterial and a second part made of a second solid material that isdifferent than the first solid material, the interferometer including abeam splitter that splits the input beam into a first intermediate beamthat has a first path through the first solid material and a secondintermediate beam that has a second path through the first solidmaterial and the second solid material, and the interferometer beingconfigured to recombine the first intermediate beam and the secondintermediate beam to produce an output beam; and a detector assemblyconfigured to receive the output beam and produce an output signal thatis dependent on an intensity of the output beam.
 13. The interferometryassembly of claim 12, wherein the first path and the second path are ofdifferent lengths and create a phase difference between the firstintermediate beam and the second intermediate beam when recombined. 14.The interferometry assembly of claim 12, wherein the first solidmaterial and the second solid material provide temperature independencefor a phase difference between the first intermediate beam and thesecond intermediate beam.
 15. The interferometry assembly of claim 12,wherein the first solid material comprises a glass, and the second solidmaterial comprises quartz.
 16. The interferometry assembly of claim 12,wherein at least a portion of the first path does not overlap with thesecond path.
 17. The interferometry assembly of claim 12, wherein theinterferometer is a Mach-Zehnder interferometer.
 18. The interferometryassembly of claim 12, wherein the interferometer is a Michelsoninterferometer.
 19. The interferometry assembly of claim 12, wherein thebeam splitter comprises an air gap.
 20. A method, comprising: receiving,by an interferometer, an input beam, the interferometer including afirst part made of a first solid material and a second part made of asecond solid material that is different than the first solid material,the interferometer including a first part made of a first solid materialand a second part made of a second solid material that is different thanthe first solid material, the interferometer including a beam splitterthat splits the input beam into a first intermediate beam that has afirst path through the first solid material and a second intermediatebeam that has a second path through the first solid material and thesecond solid material, and the interferometer being configured torecombine the first intermediate beam and the second intermediate beamto produce an output beam; and producing, by the interferometer, theoutput beam.
 21. The method of claim 20, further comprising: producing,by a detector assembly, an output signal that is dependent on anintensity of the output beam.
 22. The method of claim 20, wherein thefirst path and the second path are of different lengths and create aphase difference between the first intermediate beam and the secondintermediate beam when recombined.
 23. The method of claim 20, whereinthe first solid material and the second solid material providetemperature independence for a phase difference between the firstintermediate beam and the second intermediate beam.
 24. The method ofclaim 20, wherein the first solid material comprises a glass, and thesecond solid material comprises quartz.
 25. The method of claim 20,wherein at least a portion of the first path does not overlap with thesecond path.
 26. The method of claim 20, wherein the interferometer is aMach-Zehnder interferometer.
 27. The method of claim 20, wherein theinterferometer is a Michelson interferometer.
 28. The method of claim20, wherein the beam splitter comprises an air gap.
 29. Aninterferometer configured to receive an input beam, the interferometercomprising: a first part made of a first solid material and a secondpart made of a second solid material that is different than the firstsolid material; and a beam splitter that splits the input beam into afirst intermediate beam that has a first path through the first solidmaterial and a second intermediate beam that has a second path throughthe first solid material and the second solid material, wherein theinterferometer is configured to recombine the first intermediate beamand the second intermediate beam to produce an output beam.
 30. Theinterferometer of claim 29, wherein the first solid material and thesecond solid material provide temperature independence for a phasedifference between the first intermediate beam and the secondintermediate beam.
 31. The interferometer of claim 29, wherein the firstsolid material comprises a glass, and the second solid materialcomprises quartz.